Valuable data on quarkonia (the bound states of a heavy quark $Q=c,b$ and the corresponding antiquark) have recently been provided by a variety of sources, mainly $e^{+}{e}^{-}$ collisions, but also hadronic interactions. This permits a thorough updating of the experimental and theoretical status of electromagnetic and strong transitions in quarkonia. The $Q\overline{Q}$ transitions to other $Q\overline{Q}$ states are discussed, with some reference to processes involving $Q\overline{Q}$ annihilation.

Topological quantum computation has emerged as one of the most exciting approaches to constructing a fault-tolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as non-Abelian anyons, meaning that they obey non-Abelian braiding statistics. Quantum information is stored in states with multiple quasiparticles, which have a topological degeneracy. The unitary gate operations that are necessary for quantum computation are carried out by braiding quasiparticles and then measuring the multiquasiparticle states. The fault tolerance of a topological quantum computer arises from the nonlocal encoding of the quasiparticle states, which makes them immune to errors caused by local perturbations. To date, the only such topological states thought to have been found in nature are fractional quantum Hall states, most prominently the $\nu =5∕2$ state, although several other prospective candidates have been proposed in systems as disparate as ultracold atoms in optical lattices and thin-film superconductors. In this review article, current research in this field is described, focusing on the general theoretical concepts of non-Abelian statistics as it relates to topological quantum computation, on understanding non-Abelian quantum Hall states, on proposed experiments to detect non-Abelian anyons, and on proposed architectures for a topological quantum computer. Both the mathematical underpinnings of topological quantum computation and the physics of the subject are addressed, using the $\nu =5∕2$ fractional quantum Hall state as the archetype of a non-Abelian topological state enabling fault-tolerant quantum computation.

The recent success in quantum annealing, i.e., optimization of the cost or energy functions of complex systems utilizing quantum fluctuations is reviewed here. The concept is introduced in successive steps through studying the mapping of such computationally hard problems to classical spin-glass problems, quantum spin-glass problems arising with the introduction of quantum fluctuations, and the annealing behavior of the systems as these fluctuations are reduced slowly to zero. This provides a general framework for realizing analog quantum computation.

Experimental results for confined ${}^4\mathrm{He}$ are reviewed that are relevant to correlation-length scaling near the superfluid transition. Data are discussed for which the uniform confinement represents dimensionality crossover from three dimensions (3D) to 2D, 1D, and 0D. In addition, data for the onset of superfluidity are discussed representing 2D to 1D crossover. Collectively, these data for the specific heat, superfluid density, and thermal conductivity yield, in some cases, excellent agreement with expectations of correlation-length scaling and, in others, surprising disagreement. This is especially true in the case of 3D to 2D crossover where data are most plentiful. Here there is a clear distinction between scaling when the confined helium is normal and the lack of scaling when helium becomes superfluid. By far the most problematic result is the lack of scaling for the superfluid density for 3D to 2D crossover and, to some extent, for 3D to 1D crossover. Connectivity and proximity effects can be identified with some data. These might explain some experimental results and present opportunities for further studies of weakly coupled superfluid regions. Measurements to test the universality of finite-size effects along the superfluid transition lines as function of pressure and ${}^3\mathrm{He}$ concentration are also discussed. In the case of the specific heat, data indicate that the nonuniversal behavior of the critical exponent $\alpha$, obtained from bulk measurements, is responsible for the observation of a distinct scaling locus for confined pure ${}^4\mathrm{He}$ versus that of the confined mixtures.

In view of future plans for accurate measurements of the theoretically clean branching ratios $\mathrm{Br}(K^{+}\to {\pi }^{+}\nu \overline{\nu })$ and $\mathrm{Br}(K_L\to {\pi }^0\nu \overline{\nu })$, which should occur in the next decade, the relevant formulas for quantities of interest are collected and their theoretical and parametric uncertainties are analyzed. In addition to the angle $\beta$ in the unitarity triangle (UT), the angle $\gamma$ can also be determined from these decays with respectable precision and in this context the importance of the recent NNLO QCD calculation on the charm contribution to $K^{+}\to {\pi }^{+}\nu \overline{\nu }$ and of the improved estimate on the long-distance contribution by means of chiral perturbation theory are presented. In addition to known expressions, several new ones that should allow transparent tests of the standard model (SM) and of its extensions are presented. While the review is centered around the SM, models with minimal flavor violation and scenarios with new complex phases in decay amplitudes and meson mixing are also discussed. A review of existing results within specific extensions of the SM, in particular the littlest Higgs model with $T$-parity, $Z^{\prime }$ models, the MSSM, and a model with one universal extra dimension are given. A new “golden” relation between $B$ and $K$ systems is derived that involves $(\beta ,\gamma )$ and $\mathrm{Br}(K_L\to {\pi }^0\nu \overline{\nu })$, and the virtues of $(R_t,\beta )$, $(R_b,\gamma )$, $(\beta ,\gamma )$, and $(\overline{\eta },\gamma )$ strategies for the UT in the context of $K\to \pi \nu \overline{\nu }$ decays with the goal of testing the SM and its extensions are investigated.

This paper reviews recent experimental and theoretical progress concerning many-body phenomena in dilute, ultracold gases. It focuses on effects beyond standard weak-coupling descriptions, such as the Mott-Hubbard transition in optical lattices, strongly interacting gases in one and two dimensions, or lowest-Landau-level physics in quasi-two-dimensional gases in fast rotation. Strong correlations in fermionic gases are discussed in optical lattices or near-Feshbach resonances in the BCS-BEC crossover.

The transport of fluid in and around nanometer-sized objects with at least one characteristic dimension below $100\mathrm{nm}$ enables the occurrence of phenomena that are impossible at bigger length scales. This research field was only recently termed nanofluidics, but it has deep roots in science and technology. Nanofluidics has experienced considerable growth in recent years, as is confirmed by significant scientific and practical achievements. This review focuses on the physical properties and operational mechanisms of the most common structures, such as nanometer-sized openings and nanowires in solution on a chip. Since the surface-to-volume ratio increases with miniaturization, this ratio is high in nanochannels, resulting in surface-charge-governed transport, which allows ion separation and is described by a comprehensive electrokinetic theory. The charge selectivity is most pronounced if the Debye screening length is comparable to the smallest dimension of the nanochannel cross section, leading to a predominantly counterion containing nanometer-sized aperture. These unique properties contribute to the charge-based partitioning of biomolecules at the microchannel-nanochannel interface. Additionally, at this free-energy barrier, size-based partitioning can be achieved when biomolecules and nanoconstrictions have similar dimensions. Furthermore, nanopores and nanowires are rooted in interesting physical concepts, and since these structures demonstrate sensitive, label-free, and real-time electrical detection of biomolecules, the technologies hold great promise for the life sciences. The purpose of this review is to describe physical mechanisms on the nanometer scale where new phenomena occur, in order to exploit these unique properties and realize integrated sample preparation and analysis systems.

It has been $30\text{years}$ since the discovery of the Unruh effect. It has played a crucial role in our understanding that the particle content of a field theory is observer dependent. This effect is important in its own right and as a way to understand the phenomenon of particle emission from black holes and cosmological horizons. The Unruh effect is reviewed here with particular emphasis on its applications. A number of recent developments are also commented on and some controversies are discussed. Effort is also made to clarify what seem to be common misconceptions.

This review deals with the structure of hadrons, strongly interacting many-body systems consisting of quarks and gluons. These systems have a size of about $1\mathrm{fm}$, which shows up in scattering experiments at low momentum transfers $Q$ in the GeV region. At this scale the running coupling constant of quantum chromodynamics (QCD), the established theory of the strong interactions, becomes divergent. It is therefore highly intriguing to explore this theory in the realm of its strong interaction regime. However, the quarks and gluons cannot be resolved at the GeV scale but have to be studied through their manifestations in the bound many-body systems, for instance, pions, nucleons, and their resonances. The review starts with an overview of QCD at low momentum transfer and a summary of the theoretical apparatus describing the interaction of hadrons with electrons and photons. Experimental results are presented for the most significant observables studied with the electromagnetic probe: form factors, polarizabilities, excitation spectra, and sum rules. These experimental findings are compared and interpreted with various theoretical approaches to QCD, such as phenomenological models with quarks and pions, dispersion relations as a means to connect observables from different experiments, and, directly based on the QCD Lagrangian, chiral perturbation theory and lattice gauge theory.

This paper gives the 2006 self-consistent set of values of the basic constants and conversion factors of physics and chemistry recommended by the Committee on Data for Science and Technology (CODATA) for international use. Further, it describes in detail the adjustment of the values of the constants, including the selection of the final set of input data based on the results of least-squares analyses. The 2006 adjustment takes into account the data considered in the 2002 adjustment as well as the data that became available between 31 December 2002, the closing date of that adjustment, and 31 December 2006, the closing date of the new adjustment. The new data have led to a significant reduction in the uncertainties of many recommended values. The 2006 set replaces the previously recommended 2002 CODATA set and may also be found on the World Wide Web at physics.nist.gov/constants.

A review of $\mathit{CP}$ violation from the standard model to strings is given which includes a broad landscape of particle physics models, encompassing the nonsupersymmetric four-dimensional (4D) extensions of the standard model, and models based on supersymmetry, on extra dimensions, on strings, and on branes. The supersymmetric models discussed include complex minimal supergravity unified model and its extensions, while the models based on extra dimensions include five-dimensional models including models based on warped geometry. $\mathit{CP}$ violation beyond the standard model is central to achieving the desired amount of baryon asymmetry in the Universe via baryogenesis and leptogenesis. They also affect a variety of particle physics phenomena: electric dipole moments, $g-2$, relic density and detection rates for neutralino dark matter in supersymmetric theories, Yukawa unification in grand unified and string based models, and sparticle production cross sections, and their decay patterns and signatures at hadron colliders. Additionally $\mathit{CP}$ violations can generate $\mathit{CP}$ even–$\mathit{CP}$ odd Higgs mixings, affect the neutral Higgs spectrum, and lead to phenomena detectable at colliders. Prominent among these are the $\mathit{CP}$ violation effects in decays of neutral and charged Higgs bosons. Neutrino masses introduce new sources of $\mathit{CP}$ violation which may be explored in neutrino factories in the future. Such phases can also enter in proton stability in unified models of particle interactions. The current experimental status of $\mathit{CP}$ violation is discussed and possibilities for the future outlined.

Recent interest in aspects common to quantum information and condensed matter has prompted a flurry of activity at the border of these disciplines that were far distant until a few years ago. Numerous interesting questions have been addressed so far. Here an important part of this field, the properties of the entanglement in many-body systems, are reviewed. The zero and finite temperature properties of entanglement in interacting spin, fermion, and boson model systems are discussed. Both bipartite and multipartite entanglement will be considered. In equilibrium entanglement is shown tightly connected to the characteristics of the phase diagram. The behavior of entanglement can be related, via certain witnesses, to thermodynamic quantities thus offering interesting possibilities for an experimental test. Out of equilibrium entangled states are generated and manipulated by means of many-body Hamiltonians.

The theoretical and experimental issues relevant to neutrinoless double beta decay are reviewed. The impact that a direct observation of this exotic process would have on elementary particle physics, nuclear physics, astrophysics, and cosmology is profound. Now that neutrinos are known to have mass and experiments are becoming more sensitive, even the nonobservation of neutrinoless double beta decay will be useful. If the process is actually observed, we will immediately learn much about the neutrino. The status and discovery potential of proposed experiments are reviewed in this context, with significant emphasis on proposals favored by recent panel reviews. The importance of and challenges in the calculation of nuclear matrix elements that govern the decay are considered in detail. The increasing sensitivity of experiments and improvements in nuclear theory make the future exciting for this field at the interface of nuclear and particle physics.

The demand for coherent scattering data for modeling electron transport in matter has increased in recent years. While much effort has been devoted to the improvement of models describing electron transport and scattering, the updating of fundamental data sets on the basis of recent experimental results has often been neglected. The use of a well-validated set of electron cross sections ensures accurate calculations of transport parameters and ionization yields, with typical applications in material analysis, detector response studies, plasma diagnostics, physics of the atmosphere, and radiotherapy. Data consistency can be verified on the basis of various theoretical requirements, and systematic errors can be minimized by cross-checking results obtained from independent experiments. For example, the oscillator strength distribution of an atom can be obtained both from photoabsorption experiments and from zero-angle electron-atom collisions at high energy, on the basis of the Bethe theory. A considerable number of all electron-scattering experiments are concerned with light noble gases, in particular with argon. This gas is a dominant constituent of noble-gas discharge plasmas and plays an important role in rare-gas halide lasers and proportional scintillator counters. This work reviews electron-scattering cross sections and optical data for the argon atom, discusses the progress made in the field of electron scattering and photoabsorption, and focuses on the most appropriate criteria for verifying data consistency.

In the early 1970s, Wilson developed the concept of a fully nonperturbative renormalization group transformation. When applied to the Kondo problem, this numerical renormalization group (NRG) method gave for the first time the full crossover from the high-temperature phase of a free spin to the low-temperature phase of a completely screened spin. The NRG method was later generalized to a variety of quantum impurity problems. The purpose of this review is to give a brief introduction to the NRG method, including some guidelines for calculating physical quantities, and to survey the development of the NRG method and its various applications over the last 30 years. These applications include variants of the original Kondo problem such as the non-Fermi-liquid behavior in the two-channel Kondo model, dissipative quantum systems such as the spin-boson model, and lattice systems in the framework of the dynamical mean-field theory.

Quantum dots pose a problem where one must confront three obstacles: randomness, interactions, and finite size. Yet it is this confluence that allows one to make some theoretical advances by invoking three theoretical tools: random matrix theory, the renormalization group, and the $1∕N$ expansion. Here the reader is introduced to these techniques and shown how they may be combined to answer a set of questions pertaining to quantum dots.

A review of new developments in theoretical and experimental electronic-structure investigations of half-metallic ferromagnets (HMFs) is presented. Being semiconductors for one spin projection and metals for another, these substances are promising magnetic materials for applications in spintronics (i.e., spin-dependent electronics). Classification of HMFs by the peculiarities of their electronic structure and chemical bonding is discussed. The effects of electron-magnon interaction in HMFs and their manifestations in magnetic, spectral, thermodynamic, and transport properties are considered. Special attention is paid to the appearance of nonquasiparticle states in the energy gap, which provide an instructive example of essentially many-body features in the electronic structure. State-of-the-art electronic calculations for correlated $d$-systems are discussed, and results for specific HMFs (Heusler alloys, zinc-blende structure compounds, ${\mathrm{CrO}}_2$, and ${\mathrm{Fe}}_3{\mathrm{O}}_4$) are reviewed.

The progress in solving problems involving nonrelativistic fast ion (atom)-atom collisions with two actively participating electrons is reviewed. Such processes involve, e.g., (i) scattering between a bare nucleus (projectile) $P$ of charge $Z_P$ and a heliumlike atomic system consisting of two electrons $e_1$ and $e_2$ initially bound to the target nucleus $T$ of charge $Z_T$, i.e., the $Z_P\text{−}{(Z_T;e_1,e_2)}_i$ collisions; (ii) scattering between two hydrogenlike atoms ${(Z_P,e_1)}_{i_1}$ and ${(Z_T,e_2)}_{i_2}$, etc. A proper description of these collisional processes requires solutions of four-body problems with four active particles including two nuclei and two electrons. Among various one- as well as two-electron transitions which can occur in such collisions, special attention will be paid to double-electron capture, simultaneous transfer and ionization, simultaneous transfer and excitation, single-electron detachment and single-electron capture. Working within the four-body framework of scattering theory and imposing the proper Coulomb boundary conditions on the entrance and exit channels, the leading quantum-mechanical theories are analyzed. Both static and dynamic interelectron correlations are thoroughly examined. The correct links between scattering states and perturbation potentials are strongly emphasized. Selection of the present illustrations is dictated by the importance of interdisciplinary applications of energetic ion-atom collisions, ranging from thermonuclear fusion to medical accelerators for hadron radiotherapy.